Cassidy is a physician and Collins is a former state insurance commissioner. Both have been outspoken opponents of the House-passed American Healthcare Act, and have co-sponsored their own version of an ObamaCare repeal bill called the Patient Freedom Act.

Cassidy told The Hill he and Collins have been meeting with Senate leaders to talk about their legislation. However, he noted the politics of the Senate mean that every member’s voice matters.

“When you only have 52 senators, everybody has significant leverage. That tight vote margin means everyone is essential,” Cassidy said.

The main GOP working group on healthcare includes 13 men backed by Senate leadership who are seeking to bridge the divide between conservatives and centrists.

What ever legislation emerges from that group is likely to be the bill that comes to the Senate floor.

“Let’s look at it practically,” Capito told The Hill. “You can only lose two votes on any one issue … so I think a bloc of four or five can be very effective.”

Health lobbyists have noted many members of the leadership-led group have been fairly measured in their criticisms of the House bill approved earlier this month.

Collins and Cassidy, in contrast, both seem keen on turning sharply from the House bill.

The Maine Republican has long been seen as a potential swing vote on healthcare, while Cassidy has earned headlines for talking about a “Kimmel test” influenced by a viral monologue by late-night host Jimmy Kimmel about the need to ensure children born with health problems get the care they need.

The fact that Collins and Cassidy were not included in the leadership-led group raised eyebrows among Senate watchers and health experts.

“You can’t jam people in the Senate” and try to force them to support a bill like what happened in the House, a former Senate aide said, since the smaller group knows it can block something they don’t like.

“McConnell has to be smart about it,” the former aide said.

Collins has said she isn’t concerned about not being in the 13-member leadership group, or about the fact that it doesn’t have any women senators.

“Bill Cassidy and I are reaching out to people about our bill, so I’m not concerned about women’s voices not being heard and not being part of this very important debate,” Collins told reporters last week.

While senators are working under the assumption that there will be a cap on federal Medicaid payments, known as a per capita cap, “there’s varying degrees of willingness [among senators] to figure out how to deal with it,” said Jeannine Bender, senior director of government relations at Medicaid Health Plans of America.

In terms of making substantive progress, the Senate is essentially in a holding pattern for the next week until the Congressional Budget Office releases its analysis of how much the House bill will cost, and its impact on the insurance market. Unlike the House, the Senate needs to wait for the CBO score before voting on a bill, and that score will influence discussions moving forward.

Cassidy and Collins believe their bill is the middle ground that the House legislation failed to provide. The legislation would let states decide if they want to keep ObamaCare, or design something different while still getting the same amount of federal money. The bill would be paid for by keeping many of the ObamaCare taxes in place.

“You need income, to think you can cut $800 billion [from Medicaid] and still maintain coverage as the President promised is not compatible,” Cassidy said.

But Cassidy isn’t deterred, and said Republicans need to fulfill both their promise to repeal ObamaCare and Trump’s promises on health.

“Maybe [Republicans] aren’t interested in President Trump’s vision. But I can tell you, when he’s up for re-election, Democrats will be,” Cassidy said.

“The only way you can fulfill Trump’s contract with the voters— cover all, care for people with pre-existing conditions, get rid of mandates and lower premiums— the only way to get there and have decent coverage is through the Cassidy/Collins plan,” he added.